Question

A bag contains 12 blue balls and x red balls. If one ball is drawn at random if 8 more red balls are put in the bag, and if the probability of drawing a red ball will be twice that it will be a red ball, then find x.

Answer 1

Sample space = 12 + x

n(S) = x + 12

8 more red balls are added

Sample space = x + 12 + 8 = x + 20

Number of red balls = x + 8

Probability of drawing red ball = `(x + 8)/(x + 20)`

By the given condition

`(x + 8)/(x + 20) = 2(x/(x + 12))`

(x + 8)(x + 12) = 2x(x + 20)

x² + 20x + 96 = 2x² + 40x

x² + 20x – 96 = 0

(x + 24)(x – 4) = 0

x = − 24 or x = 4

The value of x = 4 ...(Number of balls will not be negative)

The probability of getting red balls = `(x/(x + 12))`

= `4/16`

= `1/4`